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In this paper, we consider the well‐posedness issue for the density‐dependent incompressible viscoelastic fluids of the Oldroyd model for the ideal case in space dimension greater than 2. We obtain the local well‐posedness of this model under the assumption that the initial density is bounded away from zero in the critical Besov spaces by means of the Littlewood‐Paley theory and Bony's paradifferential calculus. In particular, we obtain a Beale‐Kato‐Majida–type regularity criterion.  相似文献   

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In this paper, the Cauchy problem for the 3D diffusion approximation model in radiation hydrodynamics is considered. By using the embedding theorem and interpolation technique, we establish the global well‐posedness of strong solutions in H2.  相似文献   

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This article proposes a diffused hepatitis B virus (HBV) model with CTL immune response and nonlinear incidence for the control of viral infections. By means of different Lyapunov functions, the global asymptotical properties of the viral-free equilibrium and immune-free equilibrium of the model are obtained. Global stability of the positive equilibrium of the model is also considered. The results show that the free diffusion of the virus has no effect on the global stability of such HBV infection problem with Neumann homogeneous boundary conditions.  相似文献   

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In this paper, we construct a more general Besov spaces B ˙ r 1 , r 2 , r 3 σ , q and consider the global well‐posedness of incompressible Navier‐Stokes equations with small data in B ˙ r 1 , r 2 , r 3 σ , for 1 r 1 + 1 r 2 + 1 r 3 ? σ = 1 , 1 ? r i < . In particular, we show that for any 2 γ + 1 p 1 + 1 p 2 + 1 p 3 ? s = 1 , 1 < γ < and r i ? p i < , the solution with initial data in B ˙ r 1 , r 2 , r 3 σ , belong to L ? γ [ 0 , T ) , B ˙ p 1 , p 2 , p 3 s , , which, as far as we know, has not been discussed in other papers. Moreover, the smoothing effect of the solution to Navier‐Stokes equations is proved, which may have its own interest.  相似文献   

6.
    
This paper studies the Cauchy problem of the MHD equations with mass diffusion. We use the Tikhonov fixed point theorem to prove a local‐in‐time well‐posedness theorem. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

7.
By constructing a suitable Lyapunov function,sufficient conditions which ensure the global asymptotical stability of the positive equilibrium and boundary equilibrium of an obligate Lotka-Volterra mutualism model are obtained,respectively.It is shown that the conditions which ensure the local stability of the nonnegative equilibria is enough to ensure their global asymptotical stability.Our result supplements and complements some known result.  相似文献   

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Our aim in this paper is to study the well‐posedness of a singular reaction‐diffusion equation which is related with brain lactate kinetics, when spatial diffusion is taken into account. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

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The present work is dedicated to the well‐posedness issue of strong solutions (away from vacuum) to the compressible viscous magnetohydrodynamic (MHD) system in (d ≥ 2). We aim at extending those results in previous studies to more general Lp critical framework. Precisely, by recasting the whole system in Lagrangian coordinates, we prove the local existence and uniqueness of solutions by means of Banach fixed‐point theorem. Furthermore, with the aid of effective velocity, we employ the energy argument to establish global a priori estimates, which lead to the unique global solution near constant equilibrium. Our results hold in case of small data but large highly oscillating initial velocity and magnetic field.  相似文献   

10.
研究了一类具有扩散和Beddington-DeAngelis反应函数的病毒模型.通过构造Lyapunov函数,证明了模型的感染平衡点是全局渐近稳定的.  相似文献   

11.
    
This paper is devoted to studying the initial‐value problem of the Kawahara equation. By establishing some crucial bilinear estimates related to the Bourgain spaces Xs, b(R2) introduced by Bourgain and homogeneous Bourgain spaces, which is defined in this paper and using I‐method as well as L2 conservation law, we show that this fifth‐order shallow water wave equation is globally well‐posed for the initial data in the Sobolev spaces Hs(R) with $s{>}-frac{63}{58}$. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

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We prove the existence of global weak solution of the two‐dimensional dissipative quasi‐geostrophic equations with small initial data in and local well‐posedness with the large initial data in the same space. Our proof is based on constructing a commutator related to the problem, as well as its estimate. Copyright © 2017 John Wiley & Sons, Ltd.  相似文献   

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In this paper, we study the global well‐posedness for the two‐dimensional nonlinear Boussinesq equations with horizontal dissipation. The method we adopted is the smoothing effect in horizontal direction and the low‐high decomposition technique.  相似文献   

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In this paper, we first utilize the vanishing diffusivity method to prove the existence of global quasi‐strong solutions and get some higher order estimates, and then prove the global well‐posedness of the two‐dimensional Boussinesq system with variable viscosity for H3 initial data. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

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This paper is devoted to study the Cauchy problem for certain incompressible magnetohydrodynamics‐α model. In the Sobolev space with fractional index s>1, we proved the local solutions for any initial data, and global solutions for small initial data. Furthermore, we also prove that as α→0, the MHD‐α model reduces to the MHD equations, and the solutions of the MHD‐α model converge to a pair of solutions for the MHD equations. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

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An extension of the local projection stabilization (LPS) finite element method for convection-diffusion-reaction equations is presented and analyzed, both in the steady-state and the transient setting. In addition to the standard LPS method, a nonlinear crosswind diffusion term is introduced that accounts for the reduction of spurious oscillations. The existence of a solution can be proved and, depending on the choice of the stabilization parameter, also its uniqueness. Error estimates are derived which are supported by numerical studies. These studies demonstrate also the reduction of the spurious oscillations.https://doi.org/10.1051/m2an/2013071  相似文献   

17.
    
Hongqiu Chen 《数学研究》2016,49(2):111-131
The BBM equation posed on $mathbb{R}$ and $mathbb{R}^+$ is revisited. Improving on earlierresults, global well-posedness and bounds for the growth in time of relevant norms ofsolutions corresponding to very general auxiliary data are derived.  相似文献   

18.
    
In this paper, we consider local well‐posedness and ill‐posedness questions for the fractal Burgers equation. First, we obtain the well‐posedness result in the critical Sobolev space. We also present an unconditional uniqueness result. Second, we show the ill‐posedness from the point of view of the Picard iterations in the supercritical space. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

19.
一类具时滞生态系统的概周期解   总被引:7,自引:0,他引:7  
对具有限时滞和带扩散效应的Lotka—Volterra系统进行了研究,证明了在一定条件下系统是一致持久的,并利用建立Lyapunov函数的方法得到了系统的概周期解存在惟一和全局渐近稳定的充分条件。  相似文献   

20.
讨论了易感者类和潜伏者类均为常数输入,潜伏期、染病期和恢复期均具有传染力,且传染率为一般传染率的SEIR传染病模型.利用Hurwitz判据证明了地方病平衡点的局部渐近稳定性,进一步利用复合矩阵理论得到了地方病平衡点全局渐近稳定的充分条件.  相似文献   

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